# Tell me the answer to my math homework College

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### Tell me the answer to my math homework College

Chiefly, mathematicians use the verbal shortcut when theyre giving definitions, and then you have a hint the word being defined usually is in italics or boldface. So if you have an equation that is satisfied by some unknown number x, and you do the same thing to both sides of the equation, then the new equation will still be satisfied by the same number x. When your teacher says something that you dont understand, dont be shy about asking thats why youre in class! If youve been listening but not understanding, then your question is not a stupid question.

An equation such as says that we add together uncountably many infinitesimals, and we get a medium-sized number. For instance, everyone agrees that -- the multiplication is performed before the addition, and so the parentheses are not needed if is what you really mean to say. With or without a classmates involvement, if you think some more about the different solutions to the problem, you may learn something.

Perhaps it is just that mathematical sentences are grammatically more complicated than nonmathematical ones. And when x 2, then both sides of the inequality are defined, but the inequality is false. By going over your work i mean reading through the steps that youve just done, to see if they look right.

Of course, even aside from the issue of extraneous roots, another reason to check your answers is to avoid arithmetic errors. I think that many students would benefit from thinking of quantifiers as indicators of a competition between two adversaries, as in a court of law. Undergraduate students tend to focus on mechanical computations they are not yet mathematically mature enough to be able to think easily about theoretical and abstract ideas.

You do not need to make your handwriting as neat as this typeset document, but you need to be neat enough so that you or anyone else can distinguish easily between characters that are intended to be different. For instance, when x 6, then x 6 (or, for emphasis, x 6). When you pass a sign that says 100 miles to nashville, youre not actually in nashville yet.

This sentence involves several nested clauses, based on several quantifiers nonmathematical grammar generally doesnt involve so many nested clauses and such crucial attention to the order of the words. Can you find all of its errors? Some student actually turned this in on an exam, and expected partial credit because he had the right answer. Perhaps a more accurate explanation is this the two expressions do not actually represent individual functions rather, each of those expressions represents a of all the functions of x that can be obtained by starting with the function those two descriptions may sound different, but if you think about it, youll see that those descriptions are nevertheless specifying the same set. One disadvantage is that it may violate your teachers rules about homework being an individual effort perhaps you should ask your teacher what his or her rules are. That will usually work in calculus, but it doesnt work in differential equations, because in differential equations the c can show up anywhere -- not necessarily as a c at the end of the answer.

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## Tell me the answer to my math homework College

The timeworn and pedestrian answer is simply "to get to the other side." Here are some creative and original answers: The chicken crossed the road.
Tell me the answer to my math homework College Of course, even aside from the issue of extraneous roots, In a court of law (at least, as depicted on television), it is often the case that one side is the good guys and the other side is the bad guys, but in principle the law is supposed to be a neutral way of seeking the truth mathematical reasoning is too. If you absolutely cant think of any other method, here is a last-resort technique put the paper away somewhere. Going to dangerous places and tresp the timeworn and pedestrian answer is simply to get to the otherside. I dont know what a square dollar is, However, in some sense we add together uncountably many things when we use an integral. One easy way to do this is to put a little tail at the bottom of the , just as it appears in this typeset document, But the beginner writes neither phrase. How do you check for them? Just plug each of your answers into the original problem, Perhaps you identify with your brightest students. Here is one particularly amusing error you just have to subtract that amount from both sides of the preceding equation, Just keep careful track of your dimensions, and then see whether your answer looks right.
• ### Common Errors in College Math

The indefinite integral of a function involves an arbitrary constant, and this causes confusion for many students, because the notation doesnt convey the concept very well. For instance, which of these statements is true and which is false, using the standard real number system? For each positive number a there exists a positive number b such that b is less than a. . To put it simply some students (especially college freshmen) use the equals sign () as a symbol for the word with equal signs, where the intermediate equals signs are intended to convey equivalent to --- for example, this is very confusing and altogether wrong, because equality is transitive --- i. This is a special case of checking your work, mentioned elsewhere on this web page.

Unfortunately, some students end up with the impression that it is not necessary to check your work -- just write it up once, and hope that its correct. Perhaps the error occurred through mere carelessness, because you werent really interested in the work and you were in a hurry to finish it and put it aside. Thus, the new equation will have all the solutions x that the old equation had -- some operations are reversible -- i. Squaring both sides of an inequality is a reversible step if both sides are nonnegative. In subject, if you want to do good work, you have to work carefully, and then you have to check your work.

In fact, i am starting to think that we could avoid a lot of difficulty if we discourage beginning calculus students from using the notations the difficulty, of course, shows up when we arrive at the chain rule. Ill take this opportunity to mention that dave rusin has put together a super website, , which offers definitions, introductions, and links to all sorts of topics in math. For instance, a real-valued function f defined on the real line is continuous if for each point p and for each number epsilon greater than zero, there exists a number delta greater than zero such that, for each point q, if the distance from p to q is less than delta, then the distance from f(p) to f(q) is less than epsilon. A is used to deduce another sentence b, then sentence a should appear before sentence b. Here is why when yf(x), then dyf(x)dx is really a function of two variables-- it is a function of both x and dx. What weve just explained is that an implication and its converse generally are not equivalent. In this example, however, all the steps happen to be reversible, so those steps proofs, though it has to be used with caution, as discussed below. Of course, even aside from the issue of extraneous roots, another reason to check your answers is to avoid arithmetic errors. That certain mathematical errors are common among students may be partly a consequence of biases that are built into our language and culture, some of which we arent even aware of. And of course, for simplicitys sake, i havent mentioned the complications you run into when some problems involving infinity can be solved using the elementary arithmetic of infinity.

Here is a cute example of dimensional analysis (submitted by Benjamin Tilly). Problem: Where has my money gone? My dollar seems to have turned into a penny:

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And of course, for simplicitys sake, i havent mentioned the complications you run into when some problems involving infinity can be solved using the elementary arithmetic of infinity. Admittedly, it is a complicated looking formula, but it is preferable to a wrong formula. If you think your teacher may have made a mistake on the chalkboard, youd be doing the whole class a favor by asking about it. Ill take this opportunity to mention that dave rusin has put together a super website, , which offers definitions, introductions, and links to all sorts of topics in math. Abraham robinson invented another kind of real number system that includes nonzero infinitesimals he found a way to back up the newton-leibniz intuition with rigorous proofs Buy now Tell me the answer to my math homework College

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Because of the error, he eventually reached a point from which he could no longer proceed. Moreover, in mathematics, checking your work is an important part of the learning process. That doesnt tell us much my point here is that easy methods do work on this problem. For instance, instead of saying i do not have a lack of funds (two negatives), it is simpler to say i have sufficient funds (one positive). But if we had taken the attitude dont bother with c, just tack it on when youre done, instead of the last two steps wed have written this shows up both in differentiation and in integration.

This fact is rarely dis zeus was believed by the ancient greeks to be one of the olympian gods, and all the olympian gods lived on mt Tell me the answer to my math homework College Buy now

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It is customary to perform certain mathematical operations in certain orders, and so we dont need quite so many parentheses. Dont wait until the very end of the example, or until the end of class. For instance, some students think that their electronic calculators can be relied upon for correct answers. Here is a more complicated example following are a few different ways to say that. I recommend that beginners avoid indirect proofs as long as possible but if you continue with your math education, you will eventually run into some abstract theorems in higher math that can quantifiers are the phrases there exists and for every.

It may be a type of error that you are making with some frequency Buy Tell me the answer to my math homework College at a discount

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Thus, we arrive at the briefer formula handling constants of integration gets even more complicated in the first course on differential equations, and there are even more kinds of errors possible. You can always say more about any subject, but i just wanted to contrast the formulas as simply as possible. It can be proved that if more than countably many of those numbers being added are nonzero, the sum must be infinity. Beginners in the use of complex numbers are prone to errors such as. English or replace english with whatever is your native or local language, and so they must work to overcome the weaknesses of english.

But in many calculus textbooks, that fact is not confronted directly it is swept under the rug and hidden Buy Online Tell me the answer to my math homework College

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Unfortunately, some students end up with the impression that it is not necessary to check your work -- just write it up once, and hope that its correct. This is not an erroneous belief rather, it is a sloppy technique of writing. A formula or notation may work properly in one context, but some students try to apply it in a wider context, where it may not work properly at all. The everything is additive error is actually the most common occurrence of a more general class of errors if we can perform them in either order and get the same result. For instance, multiplication distributes over addition both on the left and on the right equal to yx.

If you absolutely cant think of any other method, here is a last-resort technique put the paper away somewhere Buy Tell me the answer to my math homework College Online at a discount

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Most people would just say the shorter sentence, and mean the longer one its a sort of verbal shortcut. One of the things that youve said has two or more possible meanings, and youre aware of that fact, but youre satisfied that its clear which meaning you intended -- either because its clear from the context, or because youve added some further, clarifying words. This web page describes the errors that i have seen most frequently in undergraduate mathematics, the likely causes of those errors, and their remedies. In fact, i am starting to think that we could avoid a lot of difficulty if we discourage beginning calculus students from using the notations the difficulty, of course, shows up when we arrive at the chain rule Tell me the answer to my math homework College For Sale

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For instance, the operation multiply both sides of the equation by 2 is reversible. Here is a correct solution into each side of the original equation, and see if the results come out the same. The latter reading suggests to some students that the answer should be a negative number, but thats not right. Ill admit that this satisfy my criterion if you got the same answer for a problem, then that answer is probably right. Here are some things worth noting multiplication is commutative -- that is, xy yx.

Use that to get using the caret symbol () for exponentiation, the calculator must replace the fractions those approximations turn out to have the same property i just mentioned for k0 For Sale Tell me the answer to my math homework College

We are to retain parts of the first question that are compatible with the new conditions, and to discard all parts of the first question that would be contradicted by the new conditions. Just as any ( must be matched with a ), so too any integral sign must be matched with a is unbalanced, and should be prohibited. For instance, represents all the integers from 1 to n, where n is some unspecified positive integer theres no way to write that the ellipsis notation conceals some terms in the sequence. Consequently, rules about division are not symmetric (though perhaps some students expected them to be symmetric). For instance, the operation multiply both sides of the equation by 2 is reversible Sale Tell me the answer to my math homework College

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